Question: Simplify the following expression: $p = \dfrac{7x^2 + 63x + 140}{x + 4} $
First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $7$ , so we can rewrite the expression: $ p =\dfrac{7(x^2 + 9x + 20)}{x + 4} $ Then we factor the remaining polynomial: $x^2 + {9}x + {20} $ ${4} + {5} = {9}$ ${4} \times {5} = {20}$ $ (x + {4}) (x + {5}) $ This gives us a factored expression: $\dfrac{7(x + {4}) (x + {5})}{x + 4}$ We can divide the numerator and denominator by $(x - 4)$ on condition that $x \neq -4$ Therefore $p = 7(x + 5); x \neq -4$